CN103324748A - Dynamic monitoring method and dynamic monitoring system for searching optimal competitive location - Google Patents

Dynamic monitoring method and dynamic monitoring system for searching optimal competitive location Download PDF

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CN103324748A
CN103324748A CN201310280206XA CN201310280206A CN103324748A CN 103324748 A CN103324748 A CN 103324748A CN 201310280206X A CN201310280206X A CN 201310280206XA CN 201310280206 A CN201310280206 A CN 201310280206A CN 103324748 A CN103324748 A CN 103324748A
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customer
limit
location
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CN103324748B (en
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姚斌
吴亦凡
李飞飞
肖小奎
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Shanghai Jiaotong University
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Abstract

The invention provides a dynamic monitoring method and a dynamic monitoring system for searching optimal competitive location. The dynamic monitoring method includes presetting a customer point set C, a facility point set F and a candidate position set P; inserting all the facility points f and customer points c into an undirected graph shown as the formula Go=(Vo,Eo) for representing a road net to divide edges of the Eo into new edges; to each point p< CUF and on consideration that the edge e where the points p located belongs to Eo, setting two end points of the e as v1 and vr, dividing the e into two parts, namely the part from the v1 to the p and the part from the p to the vr so as to make the p as a new vertex of the undirected graph, adding all the new vertexes to generate a new undirected graph shown as the formula G=(VE) with the condition that V=VoUCUF; dividing the undirected graph G into n sub graphs from G1 to Gn according to edges; acquiring the p according to the initial facility point set F and customer point set C of the undirected graph G; dynamically monitoring the p at any time according to updating of the facility point set F or customer point set C of the undirected graph G; wherein the optimal competitive location is shown as the formula; the value of the n is set according to requirements of users. By the dynamic monitoring method and the dynamic monitoring system, the optimal competitive location can be searched quickly and dynamically.

Description

Dynamic monitoring and controlling method and the system of inquiry maximum contention power position
Technical field
The present invention relates to a kind of dynamic monitoring and system of inquiring about maximum contention power position.
Background technology
In the past few years, a lot of work sutdy one classes are arranged in the situation that " the facility Placement Problems " that has a customer's location set (referring to document 8:Farahani, R.Z., Hekmatfar, M.:Facility Location:Concepts, Models, Algorithms and Case Studies, 1st edn.Physica-Verlag HD (2009), document 15:Nickel, S., Puerto, J.:Location Theory:A Unified Approach, 1st edn.Springer (2005)).In the situation that the most general, problem comprises: the set C of (1) customer's location and a facility point candidate collection P, and (2) thus in P the top condition of the satisfied predefined in position of k new facility point of inquiry.There is algorithm in the polynomial time in this class problem in the situation that k is constant, is NP-hard problem (referring to document 8 and 15) in the situation that k is general variance, and its approximate data is mainly studied in the work that has existed.
Optimum position inquiry problem can be regarded as a mutation of facility Placement Problems, and at first P is a unlimited set; Then common k=1 only that is to say and need to come chosen position for a newly-built facility point; Usually had in advance at last a facility point set F.Above these are that inquiry problem in optimum position is with respect to the difference of general " facility Placement Problems ".
The research work of optimum position inquiry problem before (referring to document 2:Cabello, S.,
Figure BDA00003463576300021
J.M., Langerman, S., Seara, C., Ventura, I.:Reverse facility location problems.In:CCCG, pp.68 – 71 (2005), document 6:Du, Y., Zhang, D., Xia, T.:The optimal-location query.In:SSTD, pp.163 – 180 (2005), document 21:Wong, R.C.W., ¨ Ozsu, T., Yu, P.S., Fu, A.W.C., Liu, L.:Efficient method for maximizing bichromatic reverse nearest neighbor.PVLDB2 (1), 1126 – 1137 (2009), document 24:Zhang, D., Du, Y., Xia, T., Tao, Y.:Progressive computation of the min-dist optimal-location query.In:VLDB, pp.643 – 654 (2006)) in what consider is the distance in the Lp space between facility point and the customer's location.Wherein people's's (referring to document 21) such as people's (referring to document 2) such as Cabello and Wong research is based on the L2 space, and people's' (referring to document 24) such as the people such as Du (referring to document 6) and Zhang research is based on the L1 space.The situation of optimum position inquiry problem in road network do not studied in these work.
Comprise in the existing research work that other two kinds are chosen relevant problem with the position of facility point: single facility point inquiry problem (referring to document 8 and 15) and facility point are set up problem in real time (referring to document 9:Fotakis, D.:Incremental algorithms for facility location and kmedian.Theor.Comput.Sci.361 (2-3), 275 – 313 (2006), document 13:Meyerson, A.:Online facility location.In:FOCS, pp.426 – 431 (2001)), these two kinds of Study on Problems contents and optimum position inquiry question marks are like still different.What single facility point was inquired about Study on Problems is, the set of a given customer's location, thereby seek a facility and set up the satisfied top condition of point, in this problem, the facility point set of not set up in the input data, yet in optimum position inquiry problem, need to consider the set of an existing facility point.What facility point was set up Study on Problems in real time is, continuous increase along with customer's location, real-time chosen position is set up new facility point and is satisfied a given optimal conditions, similar to optimum position inquiry problem is, this class problem is when seeking new facility point, also consider existing facility point set, yet [9] and [13] method of adopting can not solve optimum position inquiry problem, this is because set up in real time in the problem in facility point, the candidate locations of setting up new facility point is a limited set, but in optimum position inquiry problem, the candidate locations of setting up new facility point is a unlimited set, for example all places in the Lp space or the set in all places on all limits in the road network.We have proposed the method for optimum position in the static one query road network (referring to document 22:Xiao in the research work before us, X., Yao, B., Li, F.:Optimal location queries in road network databases.In:ICDE, pp.804 – 815 (2011)), compare with that piece article, our invention has proposed the solution of optimum position in the new Dynamic Maintenance road network, and the concrete implementation method that has been three different optimum positions inquiry Design of Problems.
At last, exist much research about querying method in the road net data storehouse in the existing research work (referring to 3:Chen, Z., Shen, H.T., Zhou, X., Yu, J.X.:Monitoring path nearest neighbor in road networks.In:SIGMOD, pp.591 – 602 (2009), document 4:Deng, K., Zhou, X., Shen, H.T., Sadiq, S., Li, X.:Instance optimal query processing in spatial networks.VLDBJ18 (3), 675 – 693 (2009), document 11:Jensen, C.S., Kol ' a ˇ rvr, J., Pedersen, T.B., Timko, I.:Nearest neighbor queries in road networks.In:GIS, pp.1 – 8 (2003), document 12:Kolahdouzan, M.R., Shahabi, C.:Voronoi-based k-nearest neighbor search for spatial network databases.In:VLDB, pp.840 – 851 (2004), document 14:Mouratidis, K., Yiu, M.L., Papadias, D., Mamoulis, N.:Continuous nearest neighbor monitoring in road networks.In:VLDB, pp.43 – 54 (2006), document 16:Papadias, D., Zhang, J., Mamoulis, N., Tao, Y.:Query processing in spatial network databases.In:VLDB, pp.802 – 813 (2003), document 17:Samet, H., Sankaranarayanan, J., Alborzi, H.:Scalable network distance browsing in spatial databases.In:SIGMOD, pp.43 – 54 (2008), document 18:Sankaranarayanan, J., Samet, H.:Distance oracles for spatial networks.In:ICDE, pp.652 – 663 (2009), document 19:Sankaranarayanan, J., Samet, H., Alborzi, H.:Path oracles for spatial networks.PVLDB2 (1), 1210 – 1221 (2009), document 23:Yiu, M.L., Mamoulis, N., Papadias, D.:Aggregate nearest neighbor queries in road networks.TKDE17 (6), 820 – 833 (2005)).Yet these research work all are inquiry (referring to document 12,16 and 17) and the mutation thereof of paying close attention to closest approach in the road net data storehouse: closest approach approximate query (referring to document 18 and 19), aggregate query (referring to document 23), continuously closest approach inquiry (referring to document 14), path closest approach inquiry (referring to document 3) etc.Technology in these research work can not solve optimum position inquiry problem, because closest approach inquiry problem and optimum position inquiry problem are different in itself.
In addition, the present invention's list of references of being correlated with also comprises as follows:
Document 1:de Berg, M., Cheong, O., van Kreveld, M., Overmars, M.:Computational Geometry:Algorithms and Applications, 3rd edn.Springer-Verlag (2008);
Document 5:Dijkstra, E.W.:A note on two problems in connexion with graphs.Numerische Mathematik1,269 – 271 (1959);
Document 7:Erwig, M., Hagen, F.:The graph voronoi diagram with applications.Networks36,156 – 163 (2000);
Document 10:Hershberger, J.:Finding the upper envelope of n line segments in o (n log n) time.Inf.Process.Lett.33 (4), 169 – 174 (1989);
Document 20:Shekhar, S., Liu, D.R.:CCAM:A connectivity-clustered access method for networks and network computations.TKDE9 (1), 102 – 119 (1997).
Summary of the invention
The object of the present invention is to provide a kind of dynamic monitoring and controlling method and system of inquiring about maximum contention power position, can be fast and dynamically inquire about maximum contention power position.
For addressing the above problem, the invention provides a kind of dynamic monitoring and controlling method of inquiring about maximum contention power position, comprising:
The set C of a given customer's location and the set F of a facility point, and a position candidate set P, maximum contention power position is
Figure BDA00003463576300051
Wherein w (c) is the weight of customer's location c, if customer's location c and facility point f are the minimal values of the point among c and the F apart from d (c, f) in road network, then define the attraction person that f is c, c is attracted by f, a (c)=d (c, f) be the attraction distance of c, C pAll customer's locations that can be attracted by p, namely
Figure BDA00003463576300052
By the undirected connected graph G to the expression road network o=(V o, E o) insert all facility point f and customer's location c with E oIn the limit be divided into new limit, for each some ρ ∈ C ∪ F, consider first the limit e ∈ E at ρ place o, making two end points of e is v lAnd v r, then e is divided into two parts namely from v lTo ρ with from ρ to v r, so that ρ becomes a new summit of undirected connected graph, add all new summits having generated a new undirected connected graph G=(V, E), and V=V o∪ C ∪ F;
G is divided into n subgraph G according to the limit 1... G n, wherein, the value of n is according to user's needs setting;
Obtain p according to facility point set F initial among the G and customer's location set C;
The renewal that occurs according to facility point set F or customer's location set C among the G is dynamic monitoring p at any time.
Further, in said method, G is divided into n subgraph G according to the limit 1... G nStep comprise:
From V, choose at random n summit as vertex set V Δ
Set up n empty subgraph G 1... G n, with vertex set V ΔIn point be made as respectively the center of each subgraph;
G and V ΔAs the input of Erwig and Hagen algorithm, calculate for each v among the G, V ΔThe nearest v ' of middle distance v and both apart from d (v, v ');
For each the bar limit e among the G, if two end points of e are to V ΔIn nearest point be same, then e is joined in the corresponding subgraph, otherwise e is joined its any one end points to V ΔIn in the subgraph of nearest some correspondence.
Further, in said method, the step of obtaining p according to facility point initial among G set F and customer's location set C comprises:
Be each subgraph G iCalculate the financial value upper limit that the position can reach in this subgraph
Figure BDA00003463576300061
Wherein, the weight sum of all customer's locations that the financial value of certain position can attract for this position, C iG iIn the set of the customer's location that a bit may attract;
Then according to this upper limit all subgraphs are sorted from high to low, sequentially travel through all subgraphs by this afterwards: for accessed subgraph, calculate the local optimum position of this subgraph and obtain corresponding financial value, wherein the local optimum position I of certain subgraph is for all have the some set of maximum return value on this subgraph; If the maximum return value of at a time current acquisition, then stops traversal greater than the financial value upper limit of next one subgraph to be visited, the position that this maximum return value is corresponding is as maximum contention power position p.
Further, in said method, be each subgraph G iCalculate the financial value upper limit that the position can reach in this subgraph
Figure BDA00003463576300071
Step comprise:
In G, add a virtual vertex v 0, from v 0To G iIn to connect a length be 0 limit each summit;
Calculate v 0Attraction set A (v 0), wherein, a given vertex v, A (v) comprises v can attract all customer's location c of arriving and the set of respective distances d (c, v);
Make C iBe A (v 0) in the set of all customer's locations of occurring;
According to C iCalculate G iThe financial value upper limit
Figure BDA00003463576300072
Further, in said method, a known vertex v, A (v) obtains as follows:
Algorithm by Erwig and Hagen calculates the nearest facility point f of each vertex v among the G and apart from d (v, f);
Initialization A (v) is empty set;
With dijkstra's algorithm according to v apart from all summits among the ascending order traversal G;
For each vertex v that traverses ', make a (v ') for v ' to the distance of its nearest facility point f, if d (v, v ')≤and a (v '), and v ' is a customer's location, then will be＜v ', d (v ', v)〉add after vertex v attracts set A (v); If d (v, v ')〉a (v '), then ignore all limits take v ' as end points.
Further, in said method, for accessed subgraph, the step of calculating the local optimum position of this subgraph and obtaining corresponding financial value comprises:
Calculate its local optimum position I and corresponding financial value m for each the bar limit e initialization in the subgraph, wherein, the local optimum position I on a certain limit e be e upper all have somes set of maximum return value;
With the local optimum position as this subgraph, the local optimum position on the limit that the maximum return value is arranged of subgraph, described maximum return value is as the corresponding financial value of this subgraph.
Further, in said method, the financial value m of its local optimum position I and correspondence of step calculate to(for) each the bar limit e initialization in the subgraph comprises:
Calculate respectively two end points v of e lAnd v rAttraction set A (v l) and A (v r);
According to the A (v that has calculated l) and A (v r) the local optimum position I of calculating e and the financial value m of correspondence.
Further, in said method, according to the A (v that has calculated l) and A (v r) calculate the local optimum position I of e and the step of corresponding financial value m comprises:
Set up an one-dimensional plane R;
For each at A (v l) the middle appearance still not at A (v r) the middle customer's location c that occurs, in R, create line segment [0, a (c)-d (c, a v l)], give weight w (c) to this line segment;
For each at A (v r) the middle appearance still not at A (v l) the middle customer's location c that occurs, in R, create line segment [l-a (c)+d (c, a v r), l], and give weight w (c), l represents the length of limit e to be calculated;
For each at A (v l) and A (v r) in the customer's location c that all occurs, if l≤2a (c)-d (c, v l)-d (c, v r), then in R, create a line segment [0, l], and give weight w (c); Otherwise, in R, create two line segment [0, a (c)-d (c, v l)] and [l-a (c)+d (c, v r), l], and give weight w (c);
Calculation level set I, I is the subset of whole piece limit [0, l], so that all cover the weight sum maximization of the line segment of I among the R;
Reentry point set I is the local optimum position on the e of limit, and corresponding financial value m is all weight sums that cover the line segment of I among the R.
Further, in said method, the renewal that occurs according to facility point set F or customer's location set C in the road network at any time step of dynamic monitoring p comprises:
The renewal of facility point and customer's location can be summed up as in the road network increases a customer's location AddC (c), reduces a customer's location DelC (c), increases a facility point AddF (f), reduces a facility point DelF (f) totally four kinds of basic operations;
When upgrading the operation arrival for one, at first calculate the set V that attracts distance can be updated the customer's location that affects cIf operation is AddC (c) or DelC (c), then V c={ c}; If operation is AddF (f) or DelF (f), then V c=c|＜c, d (c, v)〉∈ A (f) };
For each customer's location c ∈ V c, find out the attraction before of this customer's location apart from a 0(c) and new attraction apart from a ' (c), and set up two set
Figure BDA00003463576300091
With U c - = { < v , d ( c , v ) > | d ( c , v ) < a 0 ( c ) } ;
For each customer's location c ∈ V c, according to a 0(c), a ' (c), Upgrade all local optimum position I and the corresponding financial value m of each the bar limit e in calculated subgraph, local optimum position and corresponding financial value before order is upgraded are respectively I 0And m 0
Upgrade the financial value upper limit of all subgraphs;
According to the new upper limit all subgraphs are sorted from high to low, sequentially travel through all subgraphs by this afterwards:
For accessed subgraph, if this subgraph is not calculated, then local optimum position and the corresponding financial value of this subgraph if this subgraph is calculated, then directly read in the local optimum position of this subgraph of initial calculation and obtain corresponding financial value;
If the maximum return value of at a time current acquisition, then stops traversal greater than the financial value upper limit of next one subgraph to be visited, the position that this maximum return value is corresponding is as maximum contention power position p;
For the subgraph that does not traverse, as calculated subgraph wherein do not changed into calculate, think to upgrade next time and prepare.
Further, in said method, the local optimum position before the known renewal and corresponding financial value are respectively I 0And m 0, according to a 0(c), a ' (c),
Figure BDA00003463576300101
Upgrading the local optimum position I of each bar limit e and the step of corresponding financial value m comprises:
Step 1: the limit collection E of a sky of initialization 1
Step 2: for every among E limit e (v l, v r), if＜v l, d (c, v l) and＜v r, d (c, v r) person has at least one to be present in U C+And U C-And concentrate, then e is added limit collection E 1
Step 3: for limit collection E 1In each bar limit e (v l, v r) the execution following steps:
The point set I of two skies of initialization +And I -If,＜v l, d (c, v l) be present in
Figure BDA00003463576300102
In, still＜v r, d (c, v r) be not present in
Figure BDA00003463576300103
In, then to I -Line segment [0, a of middle adding 0(c)-d (c, v l)]; If＜v l, d (c, v l) be not present in
Figure BDA00003463576300104
In, still＜v r, d (c, v r) be present in
Figure BDA00003463576300105
In, then to I -Line segment [l-a of middle adding 0(c)-d (c, v r), l]; If＜v l, d (c, v l) and＜v r, d (c, v r) all be present in
Figure BDA00003463576300111
In, if l≤2a then 0(c)-d (c, v l)-d (c, v r), then to I -A line segment of middle adding [0, l], l〉2a 0(c)-d (c, v l)-d (c, v r), to I -Two line segments of middle adding [0, a (c)-d (c, v l)] and [l-a (c)+d (c, v r), l];
With obtain I -The same mode will
Figure BDA00003463576300112
Change into
Figure BDA00003463576300113
a 0(c) change a ' into (c), calculate similarly I +
If a 0(c)＜a ' (c), then an interim flag is made as ADD, calculate I '=I +-I -, otherwise, flag is made as DEL, calculate I '=I --I +
If I ' is empty set, then jump out this circulation, access limit collection E 1In next bar limit e;
If flag is ADD, then calculate I=I 0∩ I ' if I is empty set, then reinitializes the I and the m that calculate on the e; Otherwise, make m=m 0+ w (c);
If flag is DEL, if I '=[0, l], then I=I then 0, m=m 0-w (c); Otherwise, calculate I=I 0-I ' if I is empty set, then reinitializes the I and the m that calculate on the e, if I is not empty set, makes m=m 0
Make that I and m are the upper new local optimum position of limit e and corresponding financial value.
According to another side of the present invention, a kind of dynamic monitoring system of inquiring about maximum contention power position is provided, comprising:
The first definition module is used for the set C of a given customer's location and the set F of a facility point, and a position candidate set P, and maximum contention power position is Wherein w (c) is the weight of customer's location c, if customer's location c and facility point f are the minimal values of the point among c and the F apart from d (c, f) in road network, then define the attraction person that f is c, c is attracted by f, a (c)=d (c, f) be the attraction distance of c, C pAll customer's locations that can be attracted by p, namely
Figure BDA00003463576300121
Undirected connected graph is used for by the undirected connected graph G to the expression road network o=(V o, E o) insert all facility point f and customer's location c with E oIn the limit be divided into new limit, for each some ρ ∈ C ∪ F, consider first the limit e ∈ E at ρ place o, making two end points of e is v lAnd v r, then e is divided into two parts namely from v lTo ρ with from ρ to v r, so that ρ becomes a new summit of undirected connected graph, add all new summits having generated a new undirected connected graph G=(V, E), and V=V o∪ C ∪ F;
Divide module, be used for G is divided into n subgraph G according to the limit 1... G n, wherein, the value of n is according to user's needs setting;
Acquisition module is used for obtaining p according to G initial facility point set F and customer's location set C;
Update module is used at any time dynamic monitoring p of the renewal that occurs according to G facility point set F or customer's location set C.
Further, in said system, described division module is used for:
From V, choose at random n summit as vertex set V Δ
Set up n empty subgraph G 1... G n, with vertex set V ΔIn point be made as respectively the center of each subgraph;
G and V ΔAs the input of Erwig and Hagen algorithm, calculate for each v among the G, V ΔThe nearest v ' of middle distance v and both apart from d (v, v ');
For each the bar limit e among the G, if two end points of e are to V ΔIn nearest point be same, then e is joined in the corresponding subgraph, otherwise e is joined its any one end points to V ΔIn in the subgraph of nearest some correspondence.
Further, in said system, described acquisition module is used for:
Be each subgraph G iCalculate the financial value upper limit that the position can reach in this subgraph
Figure BDA00003463576300131
Wherein, the weight sum of all customer's locations that the financial value of certain position can attract for this position, C iG iIn the set of the customer's location that a bit may attract;
Then according to this upper limit all subgraphs are sorted from high to low, sequentially travel through all subgraphs by this afterwards: for accessed subgraph, calculate the local optimum position of this subgraph and obtain corresponding financial value, wherein, the local optimum position I of certain subgraph is for all have the some set of maximum return value on this subgraph; If the maximum return value of at a time current acquisition, then stops traversal greater than the financial value upper limit of next one subgraph to be visited, the position that this maximum return value is corresponding is as maximum contention power position p.
Further, in said system, described acquisition module is used for:
In G, add a virtual vertex v 0, from v 0To G iIn to connect a length be 0 limit each summit;
Calculate v 0Attraction set A (v 0), wherein, a given vertex v, A (v) comprises v can attract all customer's location c of arriving and the set of respective distances d (c, v);
Make C iBe A (v 0) in the set of all customer's locations of occurring;
According to C iCalculate G iThe financial value upper limit
Figure BDA00003463576300132
Further, in said system, a known vertex v, described acquisition module is used for obtaining A (v), specifically comprises:
Algorithm by Erwig and Hagen calculates the nearest facility point f of each vertex v among the G and apart from d (v, f);
Initialization A (v) is empty set;
With dijkstra's algorithm according to v apart from all summits among the ascending order traversal G;
For each vertex v that traverses ', make a (v ') for v ' to the distance of its nearest facility point f, if d (v, v ')≤and a (v '), and v ' is a customer's location, then will be＜v ', d (v ', v)〉add after vertex v attracts set A (v); If d (v, v ')〉a (v '), then ignore all limits take v ' as end points.
Further, in said system, described acquisition module is used for:
Calculate its local optimum position I and corresponding financial value m for each the bar limit e initialization in the subgraph, wherein, the local optimum position I on a certain limit e be e upper all have somes set of maximum return value;
With the local optimum position as this subgraph, the local optimum position on the limit that the maximum return value is arranged of subgraph, described maximum return value is as the corresponding financial value of this subgraph.
Further, in said system, described acquisition module is used for:
Calculate respectively two end points v of e lAnd v rAttraction set A (v l) and A (v r);
According to the A (v that has calculated l) and A (v r) the local optimum position I of calculating e and the financial value m of correspondence.
Further, in said system, described acquisition module is used for:
Set up an one-dimensional plane R;
For each at A (v l) the middle appearance still not at A (v r) the middle customer's location c that occurs, in R, create line segment [0, a (c)-d (c, a v l)], give weight w (c) to this line segment;
For each at A (v r) the middle appearance still not at A (v l) the middle customer's location c that occurs, in R, create line segment [l-a (c)+d (c, a v r), l], and give weight w (c), l represents the length of limit e to be calculated;
For each at A (v l) and A (v r) in the customer's location c that all occurs, if l≤2a (c)-d (c, v l)-d (c, v r), then in R, create a line segment [0, l], and give weight w (c); Otherwise, in R, create two line segment [0, a (c)-d (c, v l)] and [l-a (c)+d (c, v r), l], and give weight w (c);
Calculation level set I, I is the subset of whole piece limit [0, l], so that all cover the weight sum maximization of the line segment of I among the R;
Reentry point set I is the local optimum position on the e of limit, and corresponding financial value m is all weight sums that cover the line segment of I among the R.
Further, in said system, described update module is used for:
The renewal of facility point and customer's location can be summed up as in the road network increases a customer's location (AddC (c)), reduce a customer's location DelC (c), increase a facility point AddF (f), reduce a facility point DelF (f) totally four kinds of basic operations;
When upgrading the operation arrival for one, at first calculate the set V that attracts distance can be updated the customer's location that affects cIf operation is AddC (c) or DelC (c), then V c={ c}; If operation is AddF (f) or DelF (f), then V c=c|＜c, d (c, v)〉∈ A (f) };
For each customer's location c ∈ V c, find out the attraction before of this customer's location apart from a 0(c) and new attraction apart from a ' (c), and set up two set
Figure BDA00003463576300151
With U c - = { < v , d ( c , v ) > | d ( c , v ) < a 0 ( c ) } ;
For each customer's location c ∈ V c, according to a 0(c), a ' (c),
Figure BDA00003463576300162
Upgrade all local optimum position I and the corresponding financial value m of each the bar limit e in calculated subgraph, local optimum position and corresponding financial value before order is upgraded are respectively I 0And m 0
Upgrade the financial value upper limit of all subgraphs;
According to the new upper limit all subgraphs are sorted from high to low, sequentially travel through all subgraphs by this afterwards:
For accessed subgraph, if this subgraph is not calculated, then local optimum position and the corresponding financial value of this subgraph if this subgraph is calculated, then directly read in the local optimum position of this subgraph of initial calculation and obtain corresponding financial value;
If the maximum return value of at a time current acquisition, then stops traversal greater than the financial value upper limit of next one subgraph to be visited, the position that this maximum return value is corresponding is as maximum contention power position p;
For the subgraph that does not traverse, as calculated subgraph wherein do not changed into calculate, think to upgrade next time and prepare.
Further, in said system, the local optimum position before the known renewal and corresponding financial value are respectively I 0And m 0, described update module is used for:
The limit collection E of a sky of initialization 1
For every among E limit e (v l, v r), if＜v l, d (c, v l) and＜v r, d (c, v r) person has at least one to be present in U C+And U C-And concentrate, then e is added limit collection E 1
For limit collection E 1In each bar limit e (v l, v r) carry out following process:
The point set I of two skies of initialization +And I -If,＜v l, d (c, v l) be present in
Figure BDA00003463576300171
In, still＜v r, d (c, v r) be not present in
Figure BDA00003463576300172
In, then to I -Line segment [0, a of middle adding 0(c)-d (c, v l)]; If＜v l, d (c, v l) be not present in
Figure BDA00003463576300173
In, still＜v r, d (c, v r) be present in
Figure BDA00003463576300174
In, then to I -Line segment [l-a of middle adding 0(c)-d (c, v r), l]; If＜v l, d (c, v l) and＜v r, d (c, v r) all be present in
Figure BDA00003463576300175
In, if l≤2a then 0(c)-d (c, v l)-d (c, v r), then to I -A line segment of middle adding [0, l], l〉2a 0(c)-d (c, v l)-d (c, v r), to I -Two line segments of middle adding [0, a (c)-d (c, v l)] and [l-a (c)+d (c, v r), l];
With obtain I -The same mode will Change into
Figure BDA00003463576300177
a 0(c) change a ' into (c), calculate similarly I +
If a 0(c)＜a ' (c), then an interim flag is made as ADD, calculate I '=I +-I -, otherwise, flag is made as DEL, calculate I '=I --I +
If I ' is empty set, then jump out this circulation, access limit collection E 1In next bar limit e;
If flag is ADD, then calculate I=I 0∩ I ' if I is empty set, then reinitializes the I and the m that calculate on the e; Otherwise, make m=m 0+ w (c);
If flag is DEL, if I '=[0, l], then I=I then 0, m=m 0-w (c); Otherwise, calculate I=I 0-I ' if I is empty set, then reinitializes the I and the m that calculate on the e, if I is not empty set, makes m=m 0
Make that I and m are the upper new local optimum position of limit e and corresponding financial value.
Compared with prior art, the present invention is by the set C of a given customer's location and the set F of a facility point, and a position candidate set P, and maximum contention power position is
Figure BDA00003463576300178
Wherein w (c) is the weight of customer's location c, if customer's location c and facility point f are the minimal values of the point among c and the F apart from d (c, f) in road network, then define the attraction person that f is c, c is attracted by f, a (c)=d (c, f) be the attraction distance of c, C pAll customer's locations that can be attracted by p, namely
By the undirected connected graph G to the expression road network o=(V o, E o) insert all facility point f and customer's location c with E oIn the limit be divided into new limit, for each some ρ ∈ C ∪ F, consider first the limit e ∈ E at ρ place o, making two end points of e is v lAnd v r, then e is divided into two parts namely from v lTo ρ with from ρ to v r, so that ρ becomes a new summit of undirected connected graph, add all new summits having generated a new undirected connected graph G=(V, E), and V=V o∪ C ∪ F; G is divided into n subgraph G according to the limit 1... G n, wherein, the value of n is according to user's needs setting; Obtain p according to facility point set F initial among the G and customer's location set C; The renewal that occurs according to facility point set F or customer's location set C among the G is dynamic monitoring p at any time, can be fast and dynamically inquire about maximum contention power position.
Description of drawings
Fig. 1 is the process flow diagram of dynamic monitoring and controlling method of the inquiry maximum contention power position of one embodiment of the invention.
Embodiment
For above-mentioned purpose of the present invention, feature and advantage can be become apparent more, the present invention is further detailed explanation below in conjunction with the drawings and specific embodiments.
Embodiment one
As shown in Figure 1, the invention provides a kind of dynamic monitoring and controlling method of inquiring about maximum contention power position, comprise that step S1 is to step S4.
Step S1, the set C of a given customer's location and the set F of a facility point, and a position candidate set P, maximum contention power position is
Figure BDA00003463576300191
Wherein w (c) is the weight of customer's location c, if customer's location c and facility point f are the minimal values of the point among c and the F apart from d (c, f) in road network, then define the attraction person that f is c, c is attracted by f, a (c)=d (c, f) be the attraction distance of c, C pAll customer's locations that can be attracted by p, namely
Figure BDA00003463576300192
Step S2 is by the undirected connected graph G to the expression road network o=(V o, E o) insert all facility point f and customer's location c with E oIn the limit be divided into new limit, for each some ρ ∈ C ∪ F, consider first the limit e ∈ E at ρ place o, making two end points of e is v lAnd v r, then e is divided into two parts namely from v lTo ρ with from ρ to v r, so that ρ becomes a new summit of undirected connected graph, add all new summits having generated a new undirected connected graph G=(V, E), and V=V o∪ C ∪ F;
Step S3 is divided into n subgraph G to G according to the limit 1... G n, wherein, the value of n is according to user's needs setting;
Preferably, step S3 comprises:
From V, choose at random n summit as vertex set V Δ
Set up n empty subgraph G 1... G n, with vertex set V ΔIn point be made as respectively the center of each subgraph;
G and V ΔAs the input of Erwig and Hagen algorithm, calculate for each v among the G, V ΔThe nearest v ' of middle distance v and both apart from d (v, v ');
For each the bar limit e among the G, if two end points of e are to V ΔIn nearest point be same, then e is joined in the corresponding subgraph, otherwise e is joined its any one end points to V ΔIn in the subgraph of nearest some correspondence.
Step S4 obtains p according to facility point set F initial among the G and customer's location set C;
Preferably, step S4 comprises:
Be each subgraph G iCalculate the financial value upper limit that the position can reach in this subgraph
Figure BDA00003463576300201
Wherein, the weight sum of all customer's locations that the financial value of certain position can attract for this position, C iG iIn the set of the customer's location that a bit may attract;
Then according to this upper limit all subgraphs are sorted from high to low, sequentially travel through all subgraphs by this afterwards: for accessed subgraph, calculate the local optimum position of this subgraph and obtain corresponding financial value, wherein the local optimum position I of certain subgraph is for all have the some set of maximum return value on this subgraph; If the maximum return value of at a time current acquisition, then stops traversal greater than the financial value upper limit of next one subgraph to be visited, the position that this maximum return value is corresponding is as maximum contention power position p.
Preferably, be each subgraph G iCalculate the financial value upper limit that the position can reach in this subgraph
Figure BDA00003463576300202
Step comprise:
In G, add a virtual vertex v 0, from v 0To G iIn to connect a length be 0 limit each summit;
Calculate v 0Attraction set A (v 0), wherein, a given vertex v, A (v) comprises v can attract all customer's location c of arriving and the set of respective distances d (c, v);
Make C iBe A (v 0) in the set of all customer's locations of occurring;
According to C iCalculate G iThe financial value upper limit
Figure BDA00003463576300211
Better, a known vertex v, A (v) obtains as follows:
Algorithm by Erwig and Hagen calculates the nearest facility point f of each vertex v among the G and apart from d (v, f);
Initialization A (v) is empty set;
With dijkstra's algorithm according to v apart from all summits among the ascending order traversal G;
For each vertex v that traverses ', make a (v ') for v ' to the distance of its nearest facility point f, if d (v, v ')≤and a (v '), and v ' is a customer's location, then will be＜v ', d (v ', v)〉add after vertex v attracts set A (v); If d (v, v ')〉a (v '), then ignore all limits take v ' as end points.
Better, for accessed subgraph, the step of calculating the local optimum position of this subgraph and obtaining corresponding financial value comprises:
Calculate its local optimum position I and corresponding financial value m for each the bar limit e initialization in the subgraph, wherein, the local optimum position I on a certain limit e be e upper all have somes set of maximum return value;
With the local optimum position as this subgraph, the local optimum position on the limit that the maximum return value is arranged of subgraph, described maximum return value is as the corresponding financial value of this subgraph.
Further, the corresponding financial value m of step calculate its local optimum position I and to(for) each the bar limit e initialization in the subgraph comprises:
Calculate respectively two end points v of e lAnd v rAttraction set A (v l) and A (v r);
According to the A (v that has calculated l) and A (v r) the local optimum position I of calculating e and the financial value m of correspondence.
Better, according to the A (v that has calculated l) and A (v r) calculate the local optimum position I of e and the step of corresponding financial value m comprises:
Set up an one-dimensional plane R;
For each at A (v l) the middle appearance still not at A (v r) the middle customer's location c that occurs, in R, create line segment [0, a (c)-d (c, a v l)], give weight w (c) to this line segment;
For each at A (v r) the middle appearance still not at A (v l) the middle customer's location c that occurs, in R, create line segment [l-a (c)+d (c, a v r), l], and give weight w (c), l represents the length of limit e to be calculated;
For each at A (v l) and A (v r) in the customer's location c that all occurs, if l≤2a (c)-d (c, v l)-d (c, v r), then in R, create a line segment [0, l], and give weight w (c); Otherwise, in R, create two line segment [0, a (c)-d (c, v l)] and [l-a (c)+d (c, v r), l], and give weight w (c);
Calculation level set I, I is the subset of whole piece limit [0, l], so that all cover the weight sum maximization of the line segment of I among the R;
Reentry point set I is the local optimum position on the e of limit, and corresponding financial value m is all weight sums that cover the line segment of I among the R.
Step S5, the renewal that occurs according to facility point set F or customer's location set C among the G is dynamic monitoring p at any time.
Preferably, step S5 comprises:
The renewal of facility point and customer's location can be summed up as in the road network increases a customer's location AddC (c), reduces a customer's location DelC (c), increases a facility point AddF (f), reduces a facility point DelF (f) totally four kinds of basic operations;
When upgrading the operation arrival for one, at first calculate the set V that attracts distance can be updated the customer's location that affects cIf operation is AddC (c) or DelC (c), then V c={ c}; If operation is AddF (f) or DelF (f), then V c=c|＜c, d (c, v)〉∈ A (f) };
For each customer's location c ∈ V c, find out the attraction before of this customer's location apart from a 0(c) and new attraction apart from a ' (c), and set up two set
Figure BDA00003463576300231
With U c - = { < v , d ( c , v ) > | d ( c , v ) < a 0 ( c ) } ;
For each customer's location c ∈ V c, according to a 0(c), a ' (c),
Figure BDA00003463576300233
Upgrade all local optimum position I and the corresponding financial value m of each the bar limit e in calculated subgraph, local optimum position and corresponding financial value before order is upgraded are respectively I 0And m 0
Upgrade the financial value upper limit of all subgraphs;
According to the new upper limit all subgraphs are sorted from high to low, sequentially travel through all subgraphs by this afterwards:
For accessed subgraph, if this subgraph is not calculated, then local optimum position and the corresponding financial value of this subgraph if this subgraph is calculated, then directly read in the local optimum position of this subgraph of initial calculation and obtain corresponding financial value;
If the maximum return value of at a time current acquisition, then stops traversal greater than the financial value upper limit of next one subgraph to be visited, the position that this maximum return value is corresponding is as maximum contention power position p;
For the subgraph that does not traverse, as calculated subgraph wherein do not changed into calculate, think to upgrade next time and prepare.
Better, the local optimum position before the known renewal and corresponding financial value are respectively I 0And m 0, according to a 0(c), a ' (c),
Figure BDA00003463576300241
Upgrading the local optimum position I of each bar limit e and the step of corresponding financial value m comprises:
Step 1: the limit collection E of a sky of initialization 1
Step 2: for every among E limit e (v l, v r), if＜v l, d (c, v l) and＜v r, d (c, v r) person has at least one to be present in U C+And U C-And concentrate, then e is added limit collection E 1
Step 3: for limit collection E 1In each bar limit e (v l, v r) the execution following steps:
The point set I of two skies of initialization +And I -If,＜v l, d (c, v l) be present in In, still＜v r, d (c, v r) be not present in
Figure BDA00003463576300243
In, then to I -Line segment [0, a of middle adding 0(c)-d (c, v l)]; If＜v l, d (c, v l) be not present in In, still＜v r, d (c, v r) be present in
Figure BDA00003463576300245
In, then to I -Line segment [l-a of middle adding 0(c)-d (c, v r), l]; If＜v l, d (c, v l) and＜v r, d (c, v r) all be present in
Figure BDA00003463576300246
In, if l≤2a then 0(c)-d (c, v l)-d (c, v r), then to I -A line segment of middle adding [0, l], l〉2a 0(c)-d (c, v l)-d (c, v r), to I -Two line segments of middle adding [0, a (c)-d (c, v l)] and [l-a (c)+d (c, v r), l];
With obtain I -The same mode will
Figure BDA00003463576300247
Change into
Figure BDA00003463576300248
a 0(c) change a ' into (c), calculate similarly I +
If a 0(c)＜a ' (c), then an interim flag is made as ADD, calculate I '=I +-I -, otherwise, flag is made as DEL, calculate I '=I --I +
If I ' is empty set, then jump out this circulation, access limit collection E 1In next bar limit e;
If flag is ADD, then calculate I=I 0∩ I ' if I is empty set, then reinitializes the I and the m that calculate on the e; Otherwise, make m=m 0+ w (c);
If flag is DEL, if I '=[0, l], then I=I then 0, m=m 0-w (c); Otherwise, calculate I=I 0-I ' if I is empty set, then reinitializes the I and the m that calculate on the e, if I is not empty set, makes m=m 0
Make that I and m are the upper new local optimum position of limit e and corresponding financial value.
Embodiment two
The present invention also provides the dynamic monitoring system of another kind of inquiry maximum contention power position, comprising:
Further, in said system, the first definition module is used for the set C of a given customer's location and the set F of a facility point, and a position candidate set P, and maximum contention power position is
Figure BDA00003463576300251
Wherein w (c) is the weight of customer's location c, if customer's location c and facility point f are the minimal values of the point among c and the F apart from d (c, f) in road network, then define the attraction person that f is c, c is attracted by f, a (c)=d (c, f) be the attraction distance of c, C pAll customer's locations that can be attracted by p, namely
Undirected connected graph is used for by the undirected connected graph G to the expression road network o=(V o, E o) insert all facility point f and customer's location c with E oIn the limit be divided into new limit, for each some ρ ∈ C ∪ F, consider first the limit e ∈ E at ρ place o, making two end points of e is v lAnd v r, then e is divided into two parts namely from v lTo ρ with from ρ to v r, so that ρ becomes a new summit of undirected connected graph, add all new summits having generated a new undirected connected graph G=(V, E), and V=V o∪ C ∪ F;
Divide module, be used for G is divided into n subgraph G according to the limit 1... G n, wherein, the value of n is according to user's needs setting;
Acquisition module is used for obtaining p according to G initial facility point set F and customer's location set C;
Update module is used at any time dynamic monitoring p of the renewal that occurs according to G facility point set F or customer's location set C.
Further, in said system, described division module is used for:
From V, choose at random n summit as vertex set V Δ
Set up n empty subgraph G 1... G n, with vertex set V ΔIn point be made as respectively the center of each subgraph;
G and V ΔAs the input of Erwig and Hagen algorithm, calculate for each v among the G, V ΔThe nearest v ' of middle distance v and both apart from d (v, v ');
For each the bar limit e among the G, if two end points of e are to V ΔIn nearest point be same, then e is joined in the corresponding subgraph, otherwise e is joined its any one end points to V ΔIn in the subgraph of nearest some correspondence.
Further, in said system, described acquisition module is used for:
Be each subgraph G iCalculate the financial value upper limit that the position can reach in this subgraph
Figure BDA00003463576300261
Wherein, the weight sum of all customer's locations that the financial value of certain position can attract for this position, C iG iIn the set of the customer's location that a bit may attract;
Then according to this upper limit all subgraphs are sorted from high to low, sequentially travel through all subgraphs by this afterwards: for accessed subgraph, calculate the local optimum position of this subgraph and obtain corresponding financial value, wherein, the local optimum position I of certain subgraph is for all have the some set of maximum return value on this subgraph; If the maximum return value of at a time current acquisition, then stops traversal greater than the financial value upper limit of next one subgraph to be visited, the position that this maximum return value is corresponding is as maximum contention power position p.
Further, in said system, described acquisition module is used for:
In G, add a virtual vertex v 0, from v 0To G iIn to connect a length be 0 limit each summit;
Calculate v 0Attraction set A (v 0), wherein, a given vertex v, A (v) comprises v can attract all customer's location c of arriving and the set of respective distances d (c, v);
Make C iBe A (v 0) in the set of all customer's locations of occurring;
According to C iCalculate G iThe financial value upper limit
Figure BDA00003463576300271
Further, in said system, a known vertex v, described acquisition module is used for obtaining A (v), specifically comprises:
Algorithm by Erwig and Hagen calculates the nearest facility point f of each vertex v among the G and apart from d (v, f);
Initialization A (v) is empty set;
With dijkstra's algorithm according to v apart from all summits among the ascending order traversal G;
For each vertex v that traverses ', make a (v ') for v ' to the distance of its nearest facility point f, if d (v, v ')≤and a (v '), and v ' is a customer's location, then will be＜v ', d (v ', v)〉add after vertex v attracts set A (v); If d (v, v ')〉a (v '), then ignore all limits take v ' as end points.
Further, in said system, described acquisition module is used for:
Calculate its local optimum position I and corresponding financial value m for each the bar limit e initialization in the subgraph, wherein, the local optimum position I on a certain limit e be e upper all have somes set of maximum return value;
With the local optimum position as this subgraph, the local optimum position on the limit that the maximum return value is arranged of subgraph, described maximum return value is as the corresponding financial value of this subgraph.
Further, in said system, described acquisition module is used for:
Calculate respectively two end points v of e lAnd v rAttraction set A (v l) and A (v r);
According to the A (v that has calculated l) and A (v r) the local optimum position I of calculating e and the financial value m of correspondence.
Further, in said system, described acquisition module is used for:
Set up an one-dimensional plane R;
For each at A (v l) the middle appearance still not at A (v r) the middle customer's location c that occurs, in R, create line segment [0, a (c)-d (c, a v l)], give weight w (c) to this line segment;
For each at A (v r) the middle appearance still not at A (v l) the middle customer's location c that occurs, in R, create line segment [l-a (c)+d (c, a v r), l], and give weight w (c), l represents the length of limit e to be calculated;
For each at A (v l) and A (v r) in the customer's location c that all occurs, if l≤2a (c)-d (c, v l)-d (c, v r), then in R, create a line segment [0, l], and give weight w (c); Otherwise, in R, create two line segment [0, a (c)-d (c, v l)] and [l-a (c)+d (c, v r), l], and give weight w (c);
Calculation level set I, I is the subset of whole piece limit [0, l], so that all cover the weight sum maximization of the line segment of I among the R;
Reentry point set I is the local optimum position on the e of limit, and corresponding financial value m is all weight sums that cover the line segment of I among the R.
Further, in said system, described update module is used for:
The renewal of facility point and customer's location can be summed up as in the road network increases a customer's location (AddC (c)), reduce a customer's location DelC (c), increase a facility point AddF (f), reduce a facility point DelF (f) totally four kinds of basic operations;
When upgrading the operation arrival for one, at first calculate the set V that attracts distance can be updated the customer's location that affects cIf operation is AddC (c) or DelC (c), then V c={ c}; If operation is AddF (f) or DelF (f), then V c=c|＜c, d (c, v)〉∈ A (f) };
For each customer's location c ∈ V c, find out the attraction before of this customer's location apart from a 0(c) and new attraction apart from a ' (c), and set up two set
Figure BDA00003463576300291
With U c - = { < v , d ( c , v ) > | d ( c , v ) < a 0 ( c ) } ;
For each customer's location c ∈ V c, according to a 0(c), a ' (c),
Figure BDA00003463576300293
Upgrade all local optimum position I and the corresponding financial value m of each the bar limit e in calculated subgraph, local optimum position and corresponding financial value before order is upgraded are respectively I 0And m 0
Upgrade the financial value upper limit of all subgraphs;
According to the new upper limit all subgraphs are sorted from high to low, sequentially travel through all subgraphs by this afterwards:
For accessed subgraph, if this subgraph is not calculated, then local optimum position and the corresponding financial value of this subgraph if this subgraph is calculated, then directly read in the local optimum position of this subgraph of initial calculation and obtain corresponding financial value;
If the maximum return value of at a time current acquisition, then stops traversal greater than the financial value upper limit of next one subgraph to be visited, the position that this maximum return value is corresponding is as maximum contention power position p;
For the subgraph that does not traverse, as calculated subgraph wherein do not changed into calculate, think to upgrade next time and prepare.
Local optimum position before the known renewal and corresponding financial value are respectively I 0And m 0, described update module is used for:
The limit collection E of a sky of initialization 1
For every among E limit e (v l, v r), if＜v l, d (c, v l) and＜v r, d (c, v r) person has at least one to be present in U C+And U C-And concentrate, then e is added limit collection E 1
For limit collection E 1In each bar limit e (v l, v r) carry out following process:
The point set I of two skies of initialization +And I -If,＜v l, d (c, v l) be present in
Figure BDA00003463576300301
In, still＜v r, d (c, v r) be not present in In, then to I -Line segment [0, a of middle adding 0(c)-d (c, v l)]; If＜v l, d (c, v l) be not present in
Figure BDA00003463576300303
In, still＜v r, d (c, v r) be present in In, then to I -Line segment [l-a of middle adding 0(c)-d (c, v r), l]; If＜v l, d (c, v l) and＜v r, d (c, v r) all be present in
Figure BDA00003463576300305
In, if l≤2a then 0(c)-d (c, v l)-d (c, v r), then to I -A line segment of middle adding [0, l], l〉2a 0(c)-d (c, v l)-d (c, v r), to I -Two line segments of middle adding [0, a (c)-d (c, v l)] and [l-a (c)+d (c, v r), l];
With obtain I -The same mode will
Figure BDA00003463576300311
Change into
Figure BDA00003463576300312
a 0(c) change a ' into (c), calculate similarly I +
If a 0(c)＜a ' (c), then an interim flag is made as ADD, calculate I '=I +-I -, otherwise, flag is made as DEL, calculate I '=I --I +
If I ' is empty set, then jump out this circulation, access limit collection E 1In next bar limit e;
If flag is ADD, then calculate I=I 0∩ I ' if I is empty set, then reinitializes the I and the m that calculate on the e; Otherwise, make m=m 0+ w (c);
If flag is DEL, if I '=[0, l], then I=I then 0, m=m 0-w (c); Otherwise, calculate I=I 0-I ' if I is empty set, then reinitializes the I and the m that calculate on the e, if I is not empty set, makes m=m 0
Make that I and m are the upper new local optimum position of limit e and corresponding financial value.
Other detailed content of embodiment two specifically can referring to embodiment one, not repeat them here.
The present invention is by the set C of a given customer's location and the set F of a facility point, and a position candidate set P, and maximum contention power position is Wherein w (c) is the weight of customer's location c, if customer's location c and facility point f are the minimal values of the point among c and the F apart from d (c, f) in road network, then define the attraction person that f is c, c is attracted by f, a (c)=d (c, f) be the attraction distance of c, C pAll customer's locations that can be attracted by p, namely
Figure BDA00003463576300314
By the undirected connected graph G to the expression road network o=(V o, E o) insert all facility point f and customer's location c with E oIn the limit be divided into new limit, for each some ρ ∈ C ∪ F, consider first the limit e ∈ E at ρ place o, making two end points of e is v lAnd v r, then e is divided into two parts namely from v lTo ρ with from ρ to v r, so that ρ becomes a new summit of undirected connected graph, add all new summits having generated a new undirected connected graph G=(V, E), and V=V o∪ C ∪ F; G is divided into n subgraph G according to the limit 1... G n, wherein, the value of n is according to user's needs setting; Obtain p according to facility point set F initial among the G and customer's location set C; The renewal that occurs according to facility point set F or customer's location set C among the G is dynamic monitoring p at any time, can be fast and dynamically inquire about maximum contention power position.
Each embodiment adopts the mode of going forward one by one to describe in this instructions, and what each embodiment stressed is and the difference of other embodiment that identical similar part is mutually referring to getting final product between each embodiment.For the disclosed system of embodiment, because corresponding with the disclosed method of embodiment, so description is fairly simple, relevant part partly illustrates referring to method and gets final product.
The professional can also further recognize, unit and the algorithm steps of each example of describing in conjunction with embodiment disclosed herein, can realize with electronic hardware, computer software or the combination of the two, for the interchangeability of hardware and software clearly is described, composition and the step of each example described in general manner according to function in the above description.These functions are carried out with hardware or software mode actually, depend on application-specific and the design constraint of technical scheme.The professional and technical personnel can specifically should be used for realizing described function with distinct methods to each, but this realization should not thought and exceeds scope of the present invention.
Obviously, those skilled in the art can carry out various changes and modification to invention and not break away from the spirit and scope of the present invention.Like this, if of the present invention these revise and modification belongs within the scope of claim of the present invention and equivalent technologies thereof, then the present invention also is intended to comprise these change and modification.

Claims (20)

1. a dynamic monitoring and controlling method of inquiring about maximum contention power position is characterized in that, comprising:
The set C of a given customer's location and the set F of a facility point, and a position candidate set P, maximum contention power position is
Figure FDA00003463576200011
Wherein w (c) is the weight of customer's location c, if customer's location c and facility point f are the minimal values of the point among c and the F apart from d (c, f) in road network, then define the attraction person that f is c, c is attracted by f, a (c)=d (c, f) be the attraction distance of c, C pAll customer's locations that can be attracted by p, namely
Figure FDA00003463576200012
By the undirected connected graph G to the expression road network o=(V o, E o) insert all facility point f and customer's location c with E oIn the limit be divided into new limit, for each some ρ ∈ C ∪ F, consider first the limit e ∈ E at ρ place o, making two end points of e is v lAnd v r, then e is divided into two parts namely from v lTo ρ with from ρ to v r, so that ρ becomes a new summit of undirected connected graph, add all new summits having generated a new undirected connected graph G=(V, E), and V=V o∪ C ∪ F;
G is divided into n subgraph G according to the limit 1... G n, wherein, the value of n is according to user's needs setting;
Obtain p according to facility point set F initial among the G and customer's location set C;
The renewal that occurs according to facility point set F or customer's location set C among the G is dynamic monitoring p at any time.
2. the dynamic monitoring and controlling method of inquiry maximum contention power as claimed in claim 1 position is characterized in that, G is divided into n subgraph G according to the limit 1... G nStep comprise:
From V, choose at random n summit as vertex set V Δ
Set up n empty subgraph G 1... G n, with vertex set V ΔIn point be made as respectively the center of each subgraph;
G and V ΔAs the input of Erwig and Hagen algorithm, calculate for each v among the G, V ΔThe nearest v ' of middle distance v and both apart from d (v, v ');
For each the bar limit e among the G, if two end points of e are to V ΔIn nearest point be same, then e is joined in the corresponding subgraph, otherwise e is joined its any one end points to V ΔIn in the subgraph of nearest some correspondence.
3. the dynamic monitoring and controlling method of inquiry maximum contention power as claimed in claim 2 position is characterized in that, the step of obtaining p according to facility point set F initial among the G and customer's location set C comprises:
Be each subgraph G iCalculate the financial value upper limit that the position can reach in this subgraph
Figure FDA00003463576200021
Wherein, the weight sum of all customer's locations that the financial value of certain position can attract for this position, C iG iIn the set of the customer's location that a bit may attract;
Then according to this upper limit all subgraphs are sorted from high to low, sequentially travel through all subgraphs by this afterwards: for accessed subgraph, calculate the local optimum position of this subgraph and obtain corresponding financial value, wherein the local optimum position I of certain subgraph is for all have the some set of maximum return value on this subgraph; If the maximum return value of at a time current acquisition, then stops traversal greater than the financial value upper limit of next one subgraph to be visited, the position that this maximum return value is corresponding is as maximum contention power position p.
4. the dynamic monitoring and controlling method of inquiry maximum contention power as claimed in claim 3 position is characterized in that, is each subgraph G iCalculate the financial value upper limit that the position can reach in this subgraph
Figure FDA00003463576200022
Step comprise:
In G, add a virtual vertex v 0, from v 0To G iIn to connect a length be 0 limit each summit;
Calculate v 0Attraction set A (v 0), wherein, a given vertex v, A (v) comprises v can attract all customer's location c of arriving and the set of respective distances d (c, v);
Make C iBe A (v 0) in the set of all customer's locations of occurring;
According to C iCalculate G iThe financial value upper limit
Figure FDA00003463576200031
5. the dynamic monitoring and controlling method of inquiry maximum contention power as claimed in claim 4 position is characterized in that, a known vertex v, and A (v) obtains as follows:
Algorithm by Erwig and Hagen calculates the nearest facility point f of each vertex v among the G and apart from d (v, f);
Initialization A (v) is empty set;
With dijkstra's algorithm according to v apart from all summits among the ascending order traversal G;
For each vertex v that traverses ', make a (v ') for v ' to the distance of its nearest facility point f, if d (v, v ')≤and a (v '), and v ' is a customer's location, then will be＜v ', d (v ', v)〉add after vertex v attracts set A (v); If d (v, v ')〉a (v '), then ignore all limits take v ' as end points.
6. the dynamic monitoring and controlling method of inquiry maximum contention power as claimed in claim 5 position is characterized in that, for accessed subgraph, the step of calculating the local optimum position of this subgraph and obtaining corresponding financial value comprises:
Calculate its local optimum position I and corresponding financial value m for each the bar limit e initialization in the subgraph, wherein, the local optimum position I on a certain limit e be e upper all have somes set of maximum return value;
With the local optimum position as this subgraph, the local optimum position on the limit that the maximum return value is arranged of subgraph, described maximum return value is as the corresponding financial value of this subgraph.
7. the dynamic monitoring and controlling method of inquiry maximum contention power as claimed in claim 6 position is characterized in that, the corresponding financial value m of step calculate its local optimum position I and to(for) each the bar limit e initialization in the subgraph comprises:
Calculate respectively two end points v of e lAnd v rAttraction set A (v l) and A (v r);
According to the A (v that has calculated l) and A (v r) the local optimum position I of calculating e and the financial value m of correspondence.
8. the dynamic monitoring and controlling method of inquiry maximum contention power as claimed in claim 7 position is characterized in that, according to the A (v that has calculated l) and A (v r) calculate the local optimum position I of e and the step of corresponding financial value m comprises:
Set up an one-dimensional plane R;
For each at A (v l) the middle appearance still not at A (v r) the middle customer's location c that occurs, in R, create line segment [0, a (c)-d (c, a v l)], give weight w (c) to this line segment;
For each at A (v r) the middle appearance still not at A (v l) the middle customer's location c that occurs, in R, create line segment [l-a (c)+d (c, a v r), l], and give weight w (c), l represents the length of limit e to be calculated;
For each at A (v l) and A (v r) in the customer's location c that all occurs, if l≤2a (c)-d (c, v l)-d (c, v r), then in R, create a line segment [0, l], and give weight w (c); Otherwise, in R, create two line segment [0, a (c)-d (c, v l)] and [l-a (c)+d (c, v r), l], and give weight w (c);
Calculation level set I, I is the subset of whole piece limit [0, l], so that all cover the weight sum maximization of the line segment of I among the R;
Reentry point set I is the local optimum position on the e of limit, and corresponding financial value m is all weight sums that cover the line segment of I among the R.
9. such as the dynamic monitoring and controlling method of each described inquiry maximum contention power position of claim 1 to 8, it is characterized in that, the renewal that occurs according to facility point set F or customer's location set C in the road network at any time step of dynamic monitoring p comprises:
The renewal of facility point and customer's location can be summed up as in the road network increases a customer's location AddC (c), reduces a customer's location DelC (c), increases a facility point AddF (f), reduces a facility point DelF (f) totally four kinds of basic operations;
When upgrading the operation arrival for one, at first calculate the set V that attracts distance can be updated the customer's location that affects cIf operation is AddC (c) or DelC (c), then V c={ c}; If operation is AddF (f) or DelF (f), then V c=c|＜c, d (c, v)〉∈ A (f) };
For each customer's location c ∈ V c, find out the attraction before of this customer's location apart from a 0(c) and new attraction apart from a ' (c), and set up two set
Figure FDA00003463576200051
With U c - = { < v , d ( c , v ) > | d ( c , v ) < a 0 ( c ) } ;
For each customer's location c ∈ V c, according to a 0(c), a ' (c),
Figure FDA00003463576200053
Upgrade all local optimum position I and the corresponding financial value m of each the bar limit e in calculated subgraph, local optimum position and corresponding financial value before order is upgraded are respectively I 0And m 0
Upgrade the financial value upper limit of all subgraphs;
According to the new upper limit all subgraphs are sorted from high to low, sequentially travel through all subgraphs by this afterwards:
For accessed subgraph, if this subgraph is not calculated, then local optimum position and the corresponding financial value of this subgraph if this subgraph is calculated, then directly read in the local optimum position of this subgraph of initial calculation and obtain corresponding financial value;
If the maximum return value of at a time current acquisition, then stops traversal greater than the financial value upper limit of next one subgraph to be visited, the position that this maximum return value is corresponding is as maximum contention power position p;
For the subgraph that does not traverse, as calculated subgraph wherein do not changed into calculate, think to upgrade next time and prepare.
10. the dynamic monitoring and controlling method of inquiry maximum contention power as claimed in claim 9 position is characterized in that, the local optimum position before the known renewal and corresponding financial value are respectively I 0And m 0, according to a 0(c), a ' (c), Upgrading the local optimum position I of each bar limit e and the step of corresponding financial value m comprises:
Step 1: the limit collection E of a sky of initialization 1
Step 2: for every among E limit e (v l, v r), if＜v l, d (c, v l) and＜v r, d (c, v r) person has at least one to be present in U C+And U C-And concentrate, then e is added limit collection E 1
Step 3: for limit collection E 1In each bar limit e (v l, v r) the execution following steps:
The point set I of two skies of initialization +And I -If,＜v l, d (c, v l) be present in In, still＜v r, d (c, v r) be not present in
Figure FDA00003463576200062
In, then to I -Line segment [0, a of middle adding 0(c)-d (c, v l)]; If＜v l, d (c, v l) be not present in
Figure FDA00003463576200063
In, still＜v r, d (c, v r) be present in
Figure FDA00003463576200064
In, then to I -Line segment [l-a of middle adding 0(c)-d (c, v r), l]; If＜v l, d (c, v l) and＜v r, d (c, v r) all be present in
Figure FDA00003463576200071
In, if l≤2a then 0(c)-d (c, v l)-d (c, v r), then to I -A line segment of middle adding [0, l], l〉2a 0(c)-d (c, v l)-d (c, v r), to I -Two line segments of middle adding [0, a (c)-d (c, v l)] and [l-a (c)+d (c, v r), l];
With obtain I -The same mode will
Figure FDA00003463576200072
Change into
Figure FDA00003463576200073
a 0(c) change a ' into (c), calculate similarly I +
If a 0(c)＜a ' (c), then an interim flag is made as ADD, calculate I '=I +-I -, otherwise, flag is made as DEL, calculate I '=I --I +
If I ' is empty set, then jump out this circulation, access limit collection E 1In next bar limit e;
If flag is ADD, then calculate I=I 0∩ I ' if I is empty set, then reinitializes the I and the m that calculate on the e; Otherwise, make m=m 0+ w (c);
If flag is DEL, if I '=[0, l], then I=I then 0, m=m 0-w (c); Otherwise, calculate I=I 0-I ' if I is empty set, then reinitializes the I and the m that calculate on the e, if I is not empty set, makes m=m 0
Make that I and m are the upper new local optimum position of limit e and corresponding financial value.
11. a dynamic monitoring system of inquiring about maximum contention power position is characterized in that, comprising:
The first definition module is used for the set C of a given customer's location and the set F of a facility point, and a position candidate set P, and maximum contention power position is Wherein w (c) is the weight of customer's location c, if customer's location c and facility point f are the minimal values of the point among c and the F apart from d (c, f) in road network, then define the attraction person that f is c, c is attracted by f, a (c)=d (c, f) be the attraction distance of c, C pAll customer's locations that can be attracted by p, namely
Figure FDA00003463576200075
Undirected connected graph is used for by the undirected connected graph G to the expression road network o=(V o, E o) insert all facility point f and customer's location c with E oIn the limit be divided into new limit, for each some ρ ∈ C ∪ F, consider first the limit e ∈ E at ρ place o, making two end points of e is v lAnd v r, then e is divided into two parts namely from v lTo ρ with from ρ to v r, so that ρ becomes a new summit of undirected connected graph, add all new summits having generated a new undirected connected graph G=(V, E), and V=V o∪ C ∪ F;
Divide module, be used for G is divided into n subgraph G according to the limit 1... G n, wherein, the value of n is according to user's needs setting;
Acquisition module is used for obtaining p according to G initial facility point set F and customer's location set C;
Update module is used at any time dynamic monitoring p of the renewal that occurs according to G facility point set F or customer's location set C.
12. the dynamic monitoring system of inquiry maximum contention power as claimed in claim 11 position is characterized in that, described division module is used for:
From V, choose at random n summit as vertex set V Δ
Set up n empty subgraph G 1... G n, with vertex set V ΔIn point be made as respectively the center of each subgraph;
G and V ΔAs the input of Erwig and Hagen algorithm, calculate for each v among the G, V ΔThe nearest v ' of middle distance v and both apart from d (v, v ');
For each the bar limit e among the G, if two end points of e are to V ΔIn nearest point be same, then e is joined in the corresponding subgraph, otherwise e is joined its any one end points to V ΔIn in the subgraph of nearest some correspondence.
13. the dynamic monitoring system of inquiry maximum contention power as claimed in claim 12 position is characterized in that, described acquisition module is used for:
Be each subgraph G iCalculate the financial value upper limit that the position can reach in this subgraph
Figure FDA00003463576200091
Wherein, the weight sum of all customer's locations that the financial value of certain position can attract for this position, C iG iIn the set of the customer's location that a bit may attract;
Then according to this upper limit all subgraphs are sorted from high to low, sequentially travel through all subgraphs by this afterwards: for accessed subgraph, calculate the local optimum position of this subgraph and obtain corresponding financial value, wherein, the local optimum position I of certain subgraph is for all have the some set of maximum return value on this subgraph; If the maximum return value of at a time current acquisition, then stops traversal greater than the financial value upper limit of next one subgraph to be visited, the position that this maximum return value is corresponding is as maximum contention power position p.
14. the dynamic monitoring system of inquiry maximum contention power as claimed in claim 13 position is characterized in that, described acquisition module is used for:
In G, add a virtual vertex v 0, from v 0To G iIn to connect a length be 0 limit each summit;
Calculate v 0Attraction set A (v 0), wherein, a given vertex v, A (v) comprises v can attract all customer's location c of arriving and the set of respective distances d (c, v);
Make C iBe A (v 0) in the set of all customer's locations of occurring;
According to C iCalculate G iThe financial value upper limit
15. the dynamic monitoring system of inquiry maximum contention power as claimed in claim 14 position is characterized in that, a known vertex v, and described acquisition module is used for obtaining A (v), specifically comprises:
Algorithm by Erwig and Hagen calculates the nearest facility point f of each vertex v among the G and apart from d (v, f);
Initialization A (v) is empty set;
With dijkstra's algorithm according to v apart from all summits among the ascending order traversal G;
For each vertex v that traverses ', make a (v ') for v ' to the distance of its nearest facility point f, if d (v, v ')≤and a (v '), and v ' is a customer's location, then will be＜v ', d (v ', v)〉add after vertex v attracts set A (v); If d (v, v ')〉a (v '), then ignore all limits take v ' as end points.
16. the dynamic monitoring system of inquiry maximum contention power as claimed in claim 15 position is characterized in that, described acquisition module is used for:
Calculate its local optimum position I and corresponding financial value m for each the bar limit e initialization in the subgraph, wherein, the local optimum position I on a certain limit e be e upper all have somes set of maximum return value;
With the local optimum position as this subgraph, the local optimum position on the limit that the maximum return value is arranged of subgraph, described maximum return value is as the corresponding financial value of this subgraph.
17. the dynamic monitoring system of inquiry maximum contention power as claimed in claim 16 position is characterized in that, described acquisition module is used for:
Calculate respectively two end points v of e lAnd v rAttraction set A (v l) and A (v r);
According to the A (v that has calculated l) and A (v r) the local optimum position I of calculating e and the financial value m of correspondence.
18. the dynamic monitoring system of inquiry maximum contention power as claimed in claim 17 position is characterized in that, described acquisition module is used for:
Set up an one-dimensional plane R;
For each at A (v l) the middle appearance still not at A (v r) the middle customer's location c that occurs, in R, create line segment [0, a (c)-d (c, a v l)], give weight w (c) to this line segment;
For each at A (v r) the middle appearance still not at A (v l) the middle customer's location c that occurs, in R, create line segment [l-a (c)+d (c, a v r), l], and give weight w (c), l represents the length of limit e to be calculated;
For each at A (v l) and A (v r) in the customer's location c that all occurs, if l≤2a (c)-d (c, v l)-d (c, v r), then in R, create a line segment [0, l], and give weight w (c); Otherwise, in R, create two line segment [0, a (c)-d (c, v l)] and [l-a (c)+d (c, v r), l], and give weight w (c);
Calculation level set I, I is the subset of whole piece limit [0, l], so that all cover the weight sum maximization of the line segment of I among the R;
Reentry point set I is the local optimum position on the e of limit, and corresponding financial value m is all weight sums that cover the line segment of I among the R.
19. the dynamic monitoring system such as each described inquiry maximum contention power position of claim 11 to 18 is characterized in that, described update module is used for:
The renewal of facility point and customer's location can be summed up as in the road network increases a customer's location (AddC (c)), reduce a customer's location DelC (c), increase a facility point AddF (f), reduce a facility point DelF (f) totally four kinds of basic operations;
When upgrading the operation arrival for one, at first calculate the set V that attracts distance can be updated the customer's location that affects cIf operation is AddC (c) or DelC (c), then V c={ c}; If operation is AddF (f) or DelF (f), then V c=c|＜c, d (c, v)〉∈ A (f) };
For each customer's location c ∈ V c, find out the attraction before of this customer's location apart from a 0(c) and new attraction apart from a ' (c), and set up two set
Figure FDA00003463576200121
With U c - = { < v , d ( c , v ) > | d ( c , v ) < a 0 ( c ) } ;
For each customer's location c ∈ V c, according to a 0(c), a ' (c),
Figure FDA00003463576200123
Upgrade all local optimum position I and the corresponding financial value m of each the bar limit e in calculated subgraph, local optimum position and corresponding financial value before order is upgraded are respectively I 0And m 0
Upgrade the financial value upper limit of all subgraphs;
According to the new upper limit all subgraphs are sorted from high to low, sequentially travel through all subgraphs by this afterwards:
For accessed subgraph, if this subgraph is not calculated, then local optimum position and the corresponding financial value of this subgraph if this subgraph is calculated, then directly read in the local optimum position of this subgraph of initial calculation and obtain corresponding financial value;
If the maximum return value of at a time current acquisition, then stops traversal greater than the financial value upper limit of next one subgraph to be visited, the position that this maximum return value is corresponding is as maximum contention power position p;
For the subgraph that does not traverse, as calculated subgraph wherein do not changed into calculate, think to upgrade next time and prepare.
20. the dynamic monitoring system of inquiry maximum contention power as claimed in claim 9 position is characterized in that, the local optimum position before the known renewal and corresponding financial value are respectively I 0And m 0, described update module is used for:
The limit collection E of a sky of initialization 1
For every among E limit e (v l, v r), if＜v l, d (c, v l) and＜v r, d (c, v r) person has at least one to be present in U C+And U C-And concentrate, then e is added limit collection E 1
For limit collection E 1In each bar limit e (v l, v r) carry out following process:
The point set I of two skies of initialization +And I -If,＜v l, d (c, v l) be present in
Figure FDA00003463576200137
In, still＜v r, d (c, v r) be not present in
Figure FDA00003463576200131
In, then to I -Line segment [0, a of middle adding 0(c)-d (c, v l)]; If＜v l, d (c, v l) be not present in
Figure FDA00003463576200132
In, still＜v r, d (c, v r) be present in
Figure FDA00003463576200133
In, then to I -Line segment [l-a of middle adding 0(c)-d (c, v r), l]; If＜v l, d (c, v l) and＜v r, d (c, v r) all be present in
Figure FDA00003463576200134
In, if l≤2a then 0(c)-d (c, v l)-d (c, v r), then to I -A line segment of middle adding [0, l], l〉2a 0(c)-d (c, v l)-d (c, v r), to I -Two line segments of middle adding [0, a (c)-d (c, v l)] and [l-a (c)+d (c, v r), l];
With obtain I -The same mode will
Figure FDA00003463576200135
Change into
Figure FDA00003463576200136
a 0(c) change a ' into (c), calculate similarly I +
If a 0(c)＜a ' (c), then an interim flag is made as ADD, calculate I '=I +-I -, otherwise, flag is made as DEL, calculate I '=I --I +
If I ' is empty set, then jump out this circulation, access limit collection E 1In next bar limit e;
If flag is ADD, then calculate I=I 0∩ I ' if I is empty set, then reinitializes the I and the m that calculate on the e; Otherwise, make m=m 0+ w (c);
If flag is DEL, if I '=[0, l], then I=I then 0, m=m 0-w (c); Otherwise, calculate I=I 0-I ' if I is empty set, then reinitializes the I and the m that calculate on the e, if I is not empty set, makes m=m 0
Make that I and m are the upper new local optimum position of limit e and corresponding financial value.
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